On some spectrum estimation methods for analysis of nonstationary signals in power systems. Part I. Theoretical aspects

Frequency power converters and arc furnaces generate a wide spectrum of harmonic components and interharmonics. Representation of signals in time and frequency domain has been of interest in signal processing areas for many years, especially taking in the limelight time-varying nonstationary signals. Standard tools of harmonic analysis based on the Fourier transform assume that only harmonics are present and the periodicity intervals are fixed, while periodicity intervals in the presence of interharmonics are variable and very long. In this paper the Prony method was tested for this purpose and a novel approach for the analysis of power nonstationary signals, based on the "subspace" methods, is proposed: the "rootMusic" harmonic retrieval method which is an example of high-resolution eigenstructure-based methods. Both methods can allow an accurate and useful estimation of power quality indices as well as of the interharmonic frequencies with their changes in time. This paper, which reports the theoretical aspects of these methods, is a companion paper to a paper of the same title, Part II, in which the numerical aspects of the proposed spectrum estimation methods are analysed using nonstationary voltage and current waveforms in a supply system of a DC arc furnace.